Untitled
Gihani Dissanayake
August 18, 2017
Question 3
Practice With Association Rule Mining
Question: Pick your own thresholds for lift and confidence; just be clear what these thresholds are and how you picked them. Do your discovered item sets make sense? Present your discoveries in an interesting and concise way.
Answer:
library(arules)## Loading required package: Matrix##
## Attaching package: 'arules'## The following objects are masked from 'package:base':
##
## abbreviate, writelibrary(arulesViz)## Loading required package: gridgrocery <- read.transactions('https://raw.githubusercontent.com/jgscott/STA380/master/data/groceries.txt', sep=',')
summary(grocery)## transactions as itemMatrix in sparse format with
## 9835 rows (elements/itemsets/transactions) and
## 169 columns (items) and a density of 0.02609146
##
## most frequent items:
## whole milk other vegetables rolls/buns soda
## 2513 1903 1809 1715
## yogurt (Other)
## 1372 34055
##
## element (itemset/transaction) length distribution:
## sizes
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
## 2159 1643 1299 1005 855 645 545 438 350 246 182 117 78 77 55
## 16 17 18 19 20 21 22 23 24 26 27 28 29 32
## 46 29 14 14 9 11 4 6 1 1 1 1 3 1
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 2.000 3.000 4.409 6.000 32.000
##
## includes extended item information - examples:
## labels
## 1 abrasive cleaner
## 2 artif. sweetener
## 3 baby cosmeticsinspect(grocery[1:5])## items
## [1] {citrus fruit,
## margarine,
## ready soups,
## semi-finished bread}
## [2] {coffee,
## tropical fruit,
## yogurt}
## [3] {whole milk}
## [4] {cream cheese,
## meat spreads,
## pip fruit,
## yogurt}
## [5] {condensed milk,
## long life bakery product,
## other vegetables,
## whole milk}itemFrequencyPlot(grocery, topN = 20) 
rules <- apriori(grocery, parameter=list(support=0.01, confidence=0.5, maxlen=6))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.5 0.1 1 none FALSE TRUE 5 0.01 1
## maxlen target ext
## 6 rules FALSE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 98
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].
## sorting and recoding items ... [88 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 done [0.01s].
## writing ... [15 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].inspect(rules[1:5])## lhs rhs support confidence lift
## [1] {curd,
## yogurt} => {whole milk} 0.01006609 0.5823529 2.279125
## [2] {butter,
## other vegetables} => {whole milk} 0.01148958 0.5736041 2.244885
## [3] {domestic eggs,
## other vegetables} => {whole milk} 0.01230300 0.5525114 2.162336
## [4] {whipped/sour cream,
## yogurt} => {whole milk} 0.01087951 0.5245098 2.052747
## [5] {other vegetables,
## whipped/sour cream} => {whole milk} 0.01464159 0.5070423 1.984385inspect(subset(rules, subset=confidence > 0.8))
summary(rules)## set of 15 rules
##
## rule length distribution (lhs + rhs):sizes
## 3
## 15
##
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3 3 3 3 3 3
##
## summary of quality measures:
## support confidence lift
## Min. :0.01007 Min. :0.5000 Min. :1.984
## 1st Qu.:0.01174 1st Qu.:0.5151 1st Qu.:2.036
## Median :0.01230 Median :0.5245 Median :2.203
## Mean :0.01316 Mean :0.5411 Mean :2.299
## 3rd Qu.:0.01403 3rd Qu.:0.5718 3rd Qu.:2.432
## Max. :0.02227 Max. :0.5862 Max. :3.030
##
## mining info:
## data ntransactions support confidence
## grocery 9835 0.01 0.5After reading in the grocery dataset, we first look at the item frequency plot to look at frequent items. We randomly chosen support of 0.01 and confidence of 0.5 values to start off, but we will try different values pairs to see which balance of values will result in the number of rules that will be most beneficial for our analysis.
The items with the highest relative frequency of occurance are not surprising, as they are all items that are commonly purchased. Additionally, adise from drinks and shopping bags, all of the items with the highest frequencies are pershable, and thus need to be replaced more often.
Support = Number of transactions with both A and B / Total number of transactions=P(A∩B)
Confidence = Number of transactions with both A and B / Total number of transactions with A=P(A∩B) / P(A)
Expected Confidence = Number of transactions with B / Total number of transactions=P(B)
Lift=Confidence / Expected Confidence = P(A∩B) / P(A)*P(B)
Interactive Inspect With Datatable
Here we can experiment with different Support and Confidence values. By maintaining the Data Table form, we can see different sets for market basket analysis. When we set rules3 with support of 0.01 and confidence of 0.5, we can see 15 entries that show LHS of curd, yogurt, butter, eggs, whipped/sour cream, before buying whole milk (RHS), which makes sense as they all need to be refrigerated and therefore probably located closer together. Rules4 with support of 0.001 and confidence of 0.8 reveal much bigger datatable with 410 entries that reveal liquor, red/blush wine purchased with bottled beer which are all alcohol and make sense to buy them together and also reveals cereal as part of the pairs before buying whole milk.
As we perform more visualizations to find patterns within these baskets as well as setting different rules, we will re-adjust our confidence and support values to maximize the effectiveness of our analysis.
rules3 <- apriori(grocery, parameter=list(support=0.01, confidence=0.5))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.5 0.1 1 none FALSE TRUE 5 0.01 1
## maxlen target ext
## 10 rules FALSE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 98
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].
## sorting and recoding items ... [88 item(s)] done [0.00s].
## creating transaction tree ... done [0.00s].
## checking subsets of size 1 2 3 4 done [0.00s].
## writing ... [15 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].rules4 <- apriori(grocery, parameter=list(support=0.001, confidence=0.8))## Apriori
##
## Parameter specification:
## confidence minval smax arem aval originalSupport maxtime support minlen
## 0.8 0.1 1 none FALSE TRUE 5 0.001 1
## maxlen target ext
## 10 rules FALSE
##
## Algorithmic control:
## filter tree heap memopt load sort verbose
## 0.1 TRUE TRUE FALSE TRUE 2 TRUE
##
## Absolute minimum support count: 9
##
## set item appearances ...[0 item(s)] done [0.00s].
## set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].
## sorting and recoding items ... [157 item(s)] done [0.00s].
## creating transaction tree ... done [0.02s].
## checking subsets of size 1 2 3 4 5 6 done [0.00s].
## writing ... [410 rule(s)] done [0.00s].
## creating S4 object ... done [0.00s].inspectDT(rules3) #if we want highest support 15 entries inspectDT(rules4) #if we want wider association with 410 entriesVisualizations
rules_sorted <- sort(rules, by='confidence', decreasing=TRUE)
#matrix representation
#plot(rules[1:20], method = 'matrix', control = list(reorder=TRUE))
#Interactive Scatterplot
plotly_arules(rules)## Warning in httpuv::getRNGState(): '.Random.seed' is not an integer vector
## but of type 'NULL', so ignored#plot(rules, method = 'graph', interactive=TRUE, shading=NA)
subrules <- head(sort(rules, by='lift'),10) #Graph just 10 rules by 10 highest lifts
plot(subrules, method='graph')
plot(rules, method='grouped') #Grouped Matrix shows LHS and RHS 
plot(subrules,method='paracoord', control=list(reorder=TRUE)) #Parallel Coordinates plot for 10 rules 
The lift for {tropical fruit, root vegetables}–>{other vegetables} is very high. This means there is a strong association between these things. If we know a person bought tropical fruit and root vegetables, the person is much more likley to buy other vegetables. The support for {other vegetables,yogurt}–>{whole milk} is very high. This means there is a large proportion of all baskets that had all three of these items.
People tend to buy semi finished breads and margarine before ready soups so we should put those items close to the ready soups isle. Also, people tend to buy citrus fruit, soda, canned/bottled beer, and shopping bags before they buy margarine and ready soups.
When they buy whole milk together with ready soups, they tend to buy other vegetables. Also, people tend to buy baking powder, sugar, flour, and eggs before buying margarine, which sounds like they are buying items for baking.
Getting the product recommendation rules
rules_conf <- sort(rules, by='confidence', decreasing=TRUE)
inspect(head(rules_conf)) #High-confidence rules## lhs rhs support confidence lift
## [1] {citrus fruit,
## root vegetables} => {other vegetables} 0.01037112 0.5862069 3.029608
## [2] {root vegetables,
## tropical fruit} => {other vegetables} 0.01230300 0.5845411 3.020999
## [3] {curd,
## yogurt} => {whole milk} 0.01006609 0.5823529 2.279125
## [4] {butter,
## other vegetables} => {whole milk} 0.01148958 0.5736041 2.244885
## [5] {root vegetables,
## tropical fruit} => {whole milk} 0.01199797 0.5700483 2.230969
## [6] {root vegetables,
## yogurt} => {whole milk} 0.01453991 0.5629921 2.203354rules_lift <- sort(rules, by='lift', decreasing=TRUE)
inspect(head(rules_lift)) #High lift rules ## lhs rhs support confidence lift
## [1] {citrus fruit,
## root vegetables} => {other vegetables} 0.01037112 0.5862069 3.029608
## [2] {root vegetables,
## tropical fruit} => {other vegetables} 0.01230300 0.5845411 3.020999
## [3] {rolls/buns,
## root vegetables} => {other vegetables} 0.01220132 0.5020921 2.594890
## [4] {root vegetables,
## yogurt} => {other vegetables} 0.01291307 0.5000000 2.584078
## [5] {curd,
## yogurt} => {whole milk} 0.01006609 0.5823529 2.279125
## [6] {butter,
## other vegetables} => {whole milk} 0.01148958 0.5736041 2.244885The rules with confidence of 1 imply that, whenever the LHS item was purchased, the RHS item was also purchased 100% of the time. So in our grocery rules, if one buys citrus fruit and root vegetables, there’s 58.6% chance they will buy other vegetables.
A rule with a lift of 3 implies that, the items in LHS and RHS are 3 times more likely to be purchased together compared to the purchases when they are assumed to be unrelated, which is for the same LHS-RHS pair of {citrus fruit, root vegetables} -> {other vegetables}.
Targeting Items
- What are customers likely to buy before or after this item? What are people buying before they buy margarine?
Tend to buy bottled water, eggs, and tropic fruit. Flour and tropical fruit as lhs scored higher on support and slightly less confidence, so we consider this as well when placing items on isles or for target coupon marketing.
rules <- apriori(data=grocery, parameter=list(supp=0.001, conf=0.08), appearance = list(default = 'lhs', rhs = 'margarine'), control=list(verbose=F))
rules <- sort(rules, decreasing=TRUE, by='confidence')
inspect(rules[1:5])## lhs rhs support confidence lift
## [1] {bottled water,
## domestic eggs,
## tropical fruit} => {margarine} 0.001016777 0.4545455 7.761206
## [2] {flour,
## tropical fruit} => {margarine} 0.001423488 0.4375000 7.470161
## [3] {flour,
## whole milk,
## yogurt} => {margarine} 0.001016777 0.4000000 6.829861
## [4] {bottled water,
## flour} => {margarine} 0.001016777 0.3703704 6.323945
## [5] {flour,
## other vegetables,
## yogurt} => {margarine} 0.001016777 0.3703704 6.323945What are people buying after they buy margarine?
rules2 <- apriori(data=grocery, parameter=list(supp=0.01, conf=0.1), appearance = list(default = 'rhs', lhs = 'margarine'), control=list(verbose=F))
rules2 <- sort(rules2, by='confidence', decreasing=TRUE)
inspect(rules2)## lhs rhs support confidence lift
## [1] {margarine} => {whole milk} 0.02419929 0.4131944 1.6170980
## [2] {margarine} => {other vegetables} 0.01972547 0.3368056 1.7406635
## [3] {} => {whole milk} 0.25551601 0.2555160 1.0000000
## [4] {margarine} => {rolls/buns} 0.01474326 0.2517361 1.3686151
## [5] {margarine} => {yogurt} 0.01423488 0.2430556 1.7423115
## [6] {} => {other vegetables} 0.19349263 0.1934926 1.0000000
## [7] {margarine} => {root vegetables} 0.01108287 0.1892361 1.7361354
## [8] {} => {rolls/buns} 0.18393493 0.1839349 1.0000000
## [9] {margarine} => {bottled water} 0.01026945 0.1753472 1.5865133
## [10] {} => {soda} 0.17437722 0.1743772 1.0000000
## [11] {margarine} => {soda} 0.01016777 0.1736111 0.9956066
## [12] {} => {yogurt} 0.13950178 0.1395018 1.0000000
## [13] {} => {bottled water} 0.11052364 0.1105236 1.0000000
## [14] {} => {root vegetables} 0.10899847 0.1089985 1.0000000
## [15] {} => {tropical fruit} 0.10493137 0.1049314 1.0000000They tend to buy whole milk, other vegetables, rolls/buns, and yogurt after buying margarine. Whole milk and yogurt should be placed in the dairy section near margarine, so this chain association does make sense.